Posted on by Kalkicode
Code Matrix

Sort the major diagonal elements of a matrix

The problem is to sort the major diagonal elements of a given square matrix in ascending order. The major diagonal of a matrix consists of elements from the top-left corner to the bottom-right corner. The objective is to rearrange these diagonal elements in such a way that they are in ascending order.

Example

Consider the following matrix:

4  2  6  7  5
3  1  7  3  2
1  5  7  4  6
8  1  9  2  6
7  6  2  2  5

After sorting the major diagonal elements, the matrix becomes:

1  2  6  7  5
3  2  7  3  2
1  5  4  4  6
8  1  9  5  6
7  6  2  2  7

Idea to Solve the Problem

To solve this problem, we can traverse the major diagonal of the matrix and for each diagonal element, find the minimum element in the remaining diagonal elements and swap them. This way, we can gradually sort the major diagonal elements in ascending order.

Algorithm

  1. Display the original matrix.
  2. For each element on the major diagonal (from matrix[0][0] to matrix[N-1][N-1]), do the following: a. Find the minimum element in the remaining diagonal elements. b. Swap the current element with the found minimum element.
  3. Display the matrix after sorting the major diagonal.

Pseudocode

show_data(matrix):
    // Display matrix elements
    for i from 0 to N-1:
        for j from 0 to N-1:
            print matrix[i][j]
        print new line

swap_node(i, j, matrix):
    // Swap diagonal elements of given location
    temp = matrix[i][i]
    matrix[i][i] = matrix[j][j]
    matrix[j][j] = temp

change_element(matrix, k):
    // Set the minimum value on a given location
    min = k
    for i from k to N-1:
        if matrix[min][min] > matrix[i][i]:
            min = i
    // Set the minimum element of [k][k] position
    swap_node(k, min, matrix)

sort_major(matrix):
    // Display matrix element
    show_data(matrix)
    for k from 0 to N-1:
        change_element(matrix, k)
    // Displaying matrix element after the change
    show_data(matrix)

main:
    matrix = ...  // Define the matrix
    sort_major(matrix)

Code Solution

// C Program
// Sort the major diagonal elements of a matrix
#include <stdio.h>

#define N 5

//Display matrix elements
void show_data(int matrix[N][N])
{
    for (int i = 0; i < N; ++i)
    {
        for (int j = 0; j < N; ++j)
        {
            printf("  %d", matrix[i][j]);
        }
        printf("\n");
    }
    printf("\n");
}

// Swap diagonal elements of given location
void swap_node(int i, int j, int matrix[N][N])
{
    int temp = matrix[i][i];
    matrix[i][i] = matrix[j][j];
    matrix[j][j] = temp;
}
// Set the minimum value on a given location
void change_element(int matrix[N][N], int k)
{
    int min = k;

    for (int i = k; i < N; ++i)
    {
        if (matrix[min][min] > matrix[i][i])
        {
            min = i;
        }
    }
    // Set the minimum element of [k][k] position
    swap_node(k, min, matrix);
}
// Sort the major diagonal of a matrix
void sort_major(int matrix[N][N])
{
    // Display matrix element
    printf("\n  Before Sort Major Diagonal Element\n");
    show_data(matrix);
    for (int k = 0; k < N; ++k)
    {
        change_element(matrix, k);
    }
    // Displaying matrix element after the change
    printf(" After Sort Major Diagonal Element\n");
    show_data(matrix);
}
int main()
{
    // Test Case
    int matrix[N][N] = 
    {
        {4 , 2 , 6 , 7 , 5} ,
        {3 , 1 , 7 , 3, 2} ,
        {1 , 5 , 7,  4, 6},
        {8 , 1 ,  9,  2,  6},
        {7 , 6 ,  2,  2, 5}
    };
    sort_major(matrix);
    return 0;
}

Output

  Before Sort Major Diagonal Element
  4  2  6  7  5
  3  1  7  3  2
  1  5  7  4  6
  8  1  9  2  6
  7  6  2  2  5

 After Sort Major Diagonal Element
  1  2  6  7  5
  3  2  7  3  2
  1  5  4  4  6
  8  1  9  5  6
  7  6  2  2  7
// Include header file
#include <iostream>
#define N 5
using namespace std;
/*
  C++ Program
  Sort the major diagonal elements of a matrix
*/
class MyMatrix
{
	public:
		// Display matrix elements
		void show_data(int matrix[N][N])
		{
			for (int i = 0; i < N; ++i)
			{
				for (int j = 0; j < N; ++j)
				{
					cout << "  " << matrix[i][j];
				}
				cout << "\n";
			}
			cout << "\n";
		}
	//  Swap diagonal elements of given location
	void swap_node(int i, int j, int matrix[N][N])
	{
		int temp = matrix[i][i];
		matrix[i][i] = matrix[j][j];
		matrix[j][j] = temp;
	}
	//  Set the minimum value on a given location
	void change_element(int matrix[N][N], int k)
	{
		int min = k;
		for (int i = k; i < N; ++i)
		{
			if (matrix[min][min] > matrix[i][i])
			{
				min = i;
			}
		}
		//  Set the minimum element of [k][k] position
		this->swap_node(k, min, matrix);
	}
	//  Sort the Major diagonal of a matrix
	void sort_major(int matrix[N][N])
	{
		
		//  Display matrix element
		cout << "  Before Sort Major Diagonal Element\n";
		this->show_data(matrix);
		for (int k = 0; k < N; ++k)
		{
			this->change_element(matrix, k);
		}
		//  Display matrix element
		cout << "  After Sort Major Diagonal Element\n";
		this->show_data(matrix);
	}
};
int main()
{
	MyMatrix obj = MyMatrix();
	//  Case 1
	//  Define matrix of integer elements
	int matrix[N][N] = 
    {
          {4 , 2 , 6 , 7 , 5} ,
          {3 , 1 , 7 , 3, 2} ,
          {1 , 5 , 7,  4, 6},
          {8 , 1 ,  9,  2,  6},
          {7 , 6 ,  2,  2, 5}
    };
	obj.sort_major(matrix);

	return 0;
}

Output

  Before Sort Minor Diagonal Element
  4  2  6  7  5
  3  1  7  3  2
  1  5  7  4  6
  8  1  9  2  6
  7  6  2  2  5

  After Sort Minor Diagonal Element
  1  2  6  7  5
  3  2  7  3  2
  1  5  4  4  6
  8  1  9  5  6
  7  6  2  2  7
/* 
  Java Program
  Sort the major diagonal elements of a matrix
*/
class MyMatrix
{
    //Display matrix elements
    public void show_data(int[][] matrix,int size)
    {
        for (int i = 0; i < size; ++i)
        {
            for (int j = 0; j < size; ++j)
            {
                System.out.print("  " + matrix[i][j] );
            }
            System.out.print("\n");
        }
        System.out.print("\n");
    }
    // Swap diagonal elements of given location
    public void swap_node(int i, int j, int[][] matrix)
    {
        int temp = matrix[i][i];
        matrix[i][i] = matrix[j][j];
        matrix[j][j] = temp;
    }

    // Set the minimum value on a given location
    public void change_element(int[][] matrix, int k,int size)
    {
        int min = k;
        for (int i = k; i < size; ++i)
        {
            if (matrix[min][min] > matrix[i][i])
            {
                min = i;
            }
        }
        // Set the minimum element of [k][k] position
        swap_node(k, min, matrix);
    }

    // Sort the Major diagonal of a matrix
    public void sort_major(int[][] matrix)
    {
    
        int size = matrix.length;

        if(matrix[0].length != size || size == 0)
        {
            // Not square matrix
            return;
        }
        // Display matrix element
        System.out.print("  Before Sort Major Diagonal Element\n");
        show_data(matrix,size);
     
        for (int k = 0; k < size; ++k)
        {
            change_element(matrix, k, size);
        }
        // Display matrix element
        System.out.print("  After Sort Major Diagonal Element\n");
        show_data(matrix,size);    
    }

    public static void main(String[] args) 
    {

        MyMatrix obj = new MyMatrix();
        // Case 1
        // Define matrix of integer elements
        int[][] matrix1 =  
        {
            {4 , 2 , 6 , 7 , 5} ,
            {3 , 1 , 7 , 3, 2} ,
            {1 , 5 , 7,  4, 6},
            {8 , 1 ,  9,  2,  6},
            {7 , 6 ,  2,  2, 5}
        };
        obj.sort_major(matrix1);

        // Case 2
        // Define matrix of integer elements
        int[][] matrix2  = 
        {
            { 1 , 9 , 8 , 3 , 7 } , 
            { 3 , -1 , 5 , 3 , 8} , 
            { 1 , 3 , 5 , 6 , 11} , 
            { 0 , 9 , 8 , 6 , 2 } , 
            { 1 , 3 , 4 , 5 , 10},
        };

        obj.sort_major(matrix2);
    }
}

Output

  Before Sort Major Diagonal Element
  4  2  6  7  5
  3  1  7  3  2
  1  5  7  4  6
  8  1  9  2  6
  7  6  2  2  5

  After Sort Major Diagonal Element
  1  2  6  7  5
  3  2  7  3  2
  1  5  4  4  6
  8  1  9  5  6
  7  6  2  2  7

  Before Sort Major Diagonal Element
  1  9  8  3  7
  3  -1  5  3  8
  1  3  5  6  11
  0  9  8  6  2
  1  3  4  5  10

  After Sort Major Diagonal Element
  -1  9  8  3  7
  3  1  5  3  8
  1  3  5  6  11
  0  9  8  6  2
  1  3  4  5  10
// Include namespace system
using System;
/* 
  C# Program
  Sort the major diagonal elements of a matrix
*/
public class MyMatrix
{
	// Display matrix elements
	public void show_data(int[,] matrix, int size)
	{
		for (int i = 0; i < size; ++i)
		{
			for (int j = 0; j < size; ++j)
			{
				Console.Write("  " + matrix[i,j]);
			}
			Console.Write("\n");
		}
		Console.Write("\n");
	}
	//  Swap diagonal elements of given location
	public void swap_node(int i, int j, int[,] matrix)
	{
		int temp = matrix[i,i];
		matrix[i,i] = matrix[j,j];
		matrix[j,j] = temp;
	}
	//  Set the minimum value on a given location
	public void change_element(int[,] matrix, int k, int size)
	{
		int min = k;
		for (int i = k; i < size; ++i)
		{
			if (matrix[min,min] > matrix[i,i])
			{
				min = i;
			}
		}
		//  Set the minimum element of [k,k] position
		swap_node(k, min, matrix);
	}
	//  Sort the Major diagonal of a matrix
	public void sort_major(int[,] matrix)
	{
		int size = matrix.GetLength(0);

		if (matrix.GetLength(1) != size || size == 0)
		{
		       //  Not square matrix
			return;
		}
		//  Display matrix element
		Console.Write("  Before Sort Major Diagonal Element\n");
		show_data(matrix, size);
		for (int k = 0; k < size; ++k)
		{
			change_element(matrix, k, size);
		}
		//  Display matrix element
		Console.Write("  After Sort Major Diagonal Element\n");
		show_data(matrix, size);
	}
	public static void Main(String[] args)
	{
		MyMatrix obj = new MyMatrix();
		//  Case 1
		//  Define matrix of integer elements
		int[,] matrix1 =
        {
            {4 , 2 , 6 , 7 , 5} ,
            {3 , 1 , 7 , 3, 2} ,
            {1 , 5 , 7,  4, 6},
            {8 , 1 ,  9,  2,  6},
            {7 , 6 ,  2,  2, 5}
        };
		obj.sort_major(matrix1);
		//  Case 2
		//  Define matrix of integer elements
		int[,] matrix2 = 
        {
            { 1 , 9 , 8 , 3 , 7 } , 
            { 3 , -1 , 5 , 3 , 8} , 
            { 1 , 3 , 5 , 6 , 11} , 
            { 0 , 9 , 8 , 6 , 2 } , 
            { 1 , 3 , 4 , 5 , 10}
        };
		obj.sort_major(matrix2);
	}
}

Output

  Before Sort Major Diagonal Element
  4  2  6  7  5
  3  1  7  3  2
  1  5  7  4  6
  8  1  9  2  6
  7  6  2  2  5

  After Sort Major Diagonal Element
  1  2  6  7  5
  3  2  7  3  2
  1  5  4  4  6
  8  1  9  5  6
  7  6  2  2  7

  Before Sort Major Diagonal Element
  1  9  8  3  7
  3  -1  5  3  8
  1  3  5  6  11
  0  9  8  6  2
  1  3  4  5  10

  After Sort Major Diagonal Element
  -1  9  8  3  7
  3  1  5  3  8
  1  3  5  6  11
  0  9  8  6  2
  1  3  4  5  10
<?php
/* 
  Php Program
  Sort the major diagonal elements of a matrix
*/
class MyMatrix
{
	// Display matrix elements
	public	function show_data( & $matrix, $size)
	{
		for ($i = 0; $i < $size; ++$i)
		{
			for ($j = 0; $j < $size; ++$j)
			{
				echo "  ". $matrix[$i][$j];
			}
			echo "\n";
		}
		echo "\n";
	}
	//  Swap diagonal elements of given location
	public	function swap_node($i, $j, & $matrix)
	{
		$temp = $matrix[$i][$i];
		$matrix[$i][$i] = $matrix[$j][$j];
		$matrix[$j][$j] = $temp;
	}
	//  Set the minimum value on a given location
	public	function change_element( & $matrix, $k, $size)
	{
		$min = $k;
		for ($i = $k; $i < $size; ++$i)
		{
			if ($matrix[$min][$min] > $matrix[$i][$i])
			{
				$min = $i;
			}
		}
		//  Set the minimum element of [k][k] position
		$this->swap_node($k, $min, $matrix);
	}
	//  Sort the Major diagonal of a matrix
	public	function sort_major( & $matrix)
	{
		$size = count($matrix);

		if (count($matrix[0]) != $size || $size == 0)
		{
		        //  Not square matrix
			return;
		}
		//  Display matrix element
		echo "  Before Sort Major Diagonal Element\n";
		$this->show_data($matrix, $size);
		for ($k = 0; $k < $size; ++$k)
		{
			$this->change_element($matrix, $k, $size);
		}
		//  Display matrix element
		echo "  After Sort Major Diagonal Element\n";
		$this->show_data($matrix, $size);
	}
}

function main()
{
	$obj = new MyMatrix();
	//  Case 1
	//  Define matrix of integer elements
	$matrix1 = array(
        array(4, 2, 6, 7, 5), 
        array(3, 1, 7, 3, 2), 
        array(1, 5, 7, 4, 6), 
        array(8, 1, 9, 2, 6), 
        array(7, 6, 2, 2, 5)
    );
	$obj->sort_major($matrix1);
	//  Case 2
	//  Define matrix of integer elements
	$matrix2 = array(
        array(1, 9, 8, 3, 7), 
        array(3, -1, 5, 3, 8), 
        array(1, 3, 5, 6, 11), 
        array(0, 9, 8, 6, 2), 
        array(1, 3, 4, 5, 10)
    );
	$obj->sort_major($matrix2);
}
main();

Output

  Before Sort Major Diagonal Element
  4  2  6  7  5
  3  1  7  3  2
  1  5  7  4  6
  8  1  9  2  6
  7  6  2  2  5

  After Sort Major Diagonal Element
  1  2  6  7  5
  3  2  7  3  2
  1  5  4  4  6
  8  1  9  5  6
  7  6  2  2  7

  Before Sort Major Diagonal Element
  1  9  8  3  7
  3  -1  5  3  8
  1  3  5  6  11
  0  9  8  6  2
  1  3  4  5  10

  After Sort Major Diagonal Element
  -1  9  8  3  7
  3  1  5  3  8
  1  3  5  6  11
  0  9  8  6  2
  1  3  4  5  10
/* 
  Node Js Program
  Sort the major diagonal elements of a matrix
*/
class MyMatrix
{
	// Display matrix elements
	show_data(matrix, size)
	{
		for (var i = 0; i < size; ++i)
		{
			for (var j = 0; j < size; ++j)
			{
				process.stdout.write("  " + matrix[i][j]);
			}
			process.stdout.write("\n");
		}
		process.stdout.write("\n");
	}
	//  Swap diagonal elements of given location
	swap_node(i, j, matrix)
	{
		var temp = matrix[i][i];
		matrix[i][i] = matrix[j][j];
		matrix[j][j] = temp;
	}
	//  Set the minimum value on a given location
	change_element(matrix, k, size)
	{
		var min = k;
		for (var i = k; i < size; ++i)
		{
			if (matrix[min][min] > matrix[i][i])
			{
				min = i;
			}
		}
		//  Set the minimum element of [k][k] position
		this.swap_node(k, min, matrix);
	}
	//  Sort the Major diagonal of a matrix
	sort_major(matrix)
	{
		var size = matrix.length;

		if (matrix[0].length != size || size == 0)
		{
		        //  Not square matrix
			return;
		}
		//  Display matrix element
		process.stdout.write("  Before Sort Major Diagonal Element\n");
		this.show_data(matrix, size);
		for (var k = 0; k < size; ++k)
		{
			this.change_element(matrix, k, size);
		}
		//  Display matrix element
		process.stdout.write("  After Sort Major Diagonal Element\n");
		this.show_data(matrix, size);
	}
}

function main()
{
	var obj = new MyMatrix();
	//  Case 1
	//  Define matrix of integer elements
	var matrix1 = [
		[4, 2, 6, 7, 5] , 
        [3, 1, 7, 3, 2] , 
        [1, 5, 7, 4, 6] , 
        [8, 1, 9, 2, 6] , 
        [7, 6, 2, 2, 5]
	];
	obj.sort_major(matrix1);
	//  Case 2
	//  Define matrix of integer elements
	var matrix2 = [
		[1, 9, 8, 3, 7] , 
        [3, -1, 5, 3, 8] , 
        [1, 3, 5, 6, 11] , 
        [0, 9, 8, 6, 2] , 
        [1, 3, 4, 5, 10]
	];
	obj.sort_major(matrix2);
}
main();

Output

  Before Sort Major Diagonal Element
  4  2  6  7  5
  3  1  7  3  2
  1  5  7  4  6
  8  1  9  2  6
  7  6  2  2  5

  After Sort Major Diagonal Element
  1  2  6  7  5
  3  2  7  3  2
  1  5  4  4  6
  8  1  9  5  6
  7  6  2  2  7

  Before Sort Major Diagonal Element
  1  9  8  3  7
  3  -1  5  3  8
  1  3  5  6  11
  0  9  8  6  2
  1  3  4  5  10

  After Sort Major Diagonal Element
  -1  9  8  3  7
  3  1  5  3  8
  1  3  5  6  11
  0  9  8  6  2
  1  3  4  5  10
#  Python 3 Program
#  Sort the major diagonal elements of a matrix

class MyMatrix :
	#  Display matrix elements
	def show_data(self, matrix, size) :
		i = 0
		while (i < size) :
			j = 0
			while (j < size) :
				print("  ", matrix[i][j], end = "")
				j += 1
			
			print(end = "\n")
			i += 1
		
		print(end = "\n")
	
	#   Swap diagonal elements of given location
	def swap_node(self, i, j, matrix) :
		temp = matrix[i][i]
		matrix[i][i] = matrix[j][j]
		matrix[j][j] = temp
	
	#   Set the minimum value on a given location
	def change_element(self, matrix, k, size) :
		min = k
		i = k
		while (i < size) :
			if (matrix[min][min] > matrix[i][i]) :
				min = i
			
			i += 1
		
		#   Set the minimum element of [k][k] position
		self.swap_node(k, min, matrix)
	
	#   Sort the Major diagonal of a matrix
	def sort_major(self, matrix) :
		size = len(matrix)

		if (len(matrix[0]) != size or size == 0) :
		       #   Not square matrix
			return
		
		#   Display matrix element
		print("  Before Sort Major Diagonal Element")
		self.show_data(matrix, size)
		k = 0
		while (k < size) :
			self.change_element(matrix, k, size)
			k += 1
		
		#   Display matrix element
		print("  After Sort Major Diagonal Element")
		self.show_data(matrix, size)
	

def main() :
	obj = MyMatrix()
	#   Case 1
	#   Define matrix of integer elements
	matrix1 = [
		[4, 2, 6, 7, 5] , 
        [3, 1, 7, 3, 2] , 
        [1, 5, 7, 4, 6] , 
        [8, 1, 9, 2, 6] , 
        [7, 6, 2, 2, 5]
	]
	obj.sort_major(matrix1)
	#   Case 2
	#   Define matrix of integer elements
	matrix2 = [
		[1, 9, 8, 3, 7] , 
        [3, -1, 5, 3, 8] , 
        [1, 3, 5, 6, 11] , 
        [0, 9, 8, 6, 2] , 
        [1, 3, 4, 5, 10]
	]
	obj.sort_major(matrix2)

if __name__ == "__main__": main()

Output

  Before Sort Major Diagonal Element
   4   2   6   7   5
   3   1   7   3   2
   1   5   7   4   6
   8   1   9   2   6
   7   6   2   2   5

  After Sort Major Diagonal Element
   1   2   6   7   5
   3   2   7   3   2
   1   5   4   4   6
   8   1   9   5   6
   7   6   2   2   7

  Before Sort Major Diagonal Element
   1   9   8   3   7
   3   -1   5   3   8
   1   3   5   6   11
   0   9   8   6   2
   1   3   4   5   10

  After Sort Major Diagonal Element
   -1   9   8   3   7
   3   1   5   3   8
   1   3   5   6   11
   0   9   8   6   2
   1   3   4   5   10
#   Ruby Program
#   Sort the major diagonal elements of a matrix

class MyMatrix 
	#  Display matrix elements
	def show_data(matrix, size) 
		i = 0
		while (i < size) 
			j = 0
			while (j < size) 
				print("  ", matrix[i][j])
				j += 1
			end

			print("\n")
			i += 1
		end

		print("\n")
	end

	#   Swap diagonal elements of given location
	def swap_node(i, j, matrix) 
		temp = matrix[i][i]
		matrix[i][i] = matrix[j][j]
		matrix[j][j] = temp
	end

	#   Set the minimum value on a given location
	def change_element(matrix, k, size) 
		min = k
		i = k
		while (i < size) 
			if (matrix[min][min] > matrix[i][i]) 
				min = i
			end

			i += 1
		end

		#   Set the minimum element of [k][k] position
		self.swap_node(k, min, matrix)
	end

	#   Sort the Major diagonal of a matrix
	def sort_major(matrix) 
		size = matrix.length

		if (matrix[0].length != size || size == 0)
		       #   Not square matrix 
			return
		end

		# Display matrix element
		print("  Before Sort Major Diagonal Element\n")
		self.show_data(matrix, size)
		k = 0
		while (k < size) 
			self.change_element(matrix, k, size)
			k += 1
		end

		# Display matrix element
		print("  After Sort Major Diagonal Element\n")
		self.show_data(matrix, size)
	end

end

def main() 
	obj = MyMatrix.new()
	#   Case 1
	#   Define matrix of integer elements
	matrix1 = [
		[4, 2, 6, 7, 5] , 
        [3, 1, 7, 3, 2] , 
        [1, 5, 7, 4, 6] , 
        [8, 1, 9, 2, 6] ,
        [7, 6, 2, 2, 5]
	]
	obj.sort_major(matrix1)
	#   Case 2
	#   Define matrix of integer elements
	matrix2 = [
		[1, 9, 8, 3, 7] , 
        [3, -1, 5, 3, 8] , 
        [1, 3, 5, 6, 11] , 
        [0, 9, 8, 6, 2] , 
        [1, 3, 4, 5, 10]
	]
	obj.sort_major(matrix2)
end

main()

Output

  Before Sort Major Diagonal Element
  4  2  6  7  5
  3  1  7  3  2
  1  5  7  4  6
  8  1  9  2  6
  7  6  2  2  5

  After Sort Major Diagonal Element
  1  2  6  7  5
  3  2  7  3  2
  1  5  4  4  6
  8  1  9  5  6
  7  6  2  2  7

  Before Sort Major Diagonal Element
  1  9  8  3  7
  3  -1  5  3  8
  1  3  5  6  11
  0  9  8  6  2
  1  3  4  5  10

  After Sort Major Diagonal Element
  -1  9  8  3  7
  3  1  5  3  8
  1  3  5  6  11
  0  9  8  6  2
  1  3  4  5  10

/* 
  Scala Program
  Sort the major diagonal elements of a matrix
*/
class MyMatrix
{
	//  Display matrix elements
	def show_data(matrix: Array[Array[Int]], size: Int): Unit = {
		var i: Int = 0;
		while (i < size)
		{
			var j: Int = 0;
			while (j < size)
			{
				print("  " + matrix(i)(j));
				j += 1;
			}
			print("\n");
			i += 1;
		}
		print("\n");
	}
	//   Swap diagonal elements of given location
	def swap_node(i: Int, j: Int, matrix: Array[Array[Int]]): Unit = {
		var temp: Int = matrix(i)(i);
		matrix(i)(i) = matrix(j)(j);
		matrix(j)(j) = temp;
	}
	//   Set the minimum value on a given location
	def change_element(matrix: Array[Array[Int]], k: Int, size: Int): Unit = {
		var min: Int = k;
		var i: Int = k;
		while (i < size)
		{
			if (matrix(min)(min) > matrix(i)(i))
			{
				min = i;
			}
			i += 1;
		}
		//   Set the minimum element of [k][k] position
		this.swap_node(k, min, matrix);
	}
	//   Sort the Major diagonal of a matrix
	def sort_major(matrix: Array[Array[Int]]): Unit = {
		var size: Int = matrix.length;
		
		if (matrix(0).length != size || size == 0)
		{
          	       // Not square matrix
			return;
		}
		//   Display matrix element
		print("  Before Sort Major Diagonal Element\n");
		this.show_data(matrix, size);
		var k: Int = 0;
		while (k < size)
		{
			this.change_element(matrix, k, size);
			k += 1;
		}
		//   Display matrix element
		print("  After Sort Major Diagonal Element\n");
		this.show_data(matrix, size);
	}
}
object Main
{
	def main(args: Array[String]): Unit = {
		var obj: MyMatrix = new MyMatrix();
		//   Case 1
		//   Define matrix of integer elements
		var matrix1: Array[Array[Int]] = Array(
            Array(4, 2, 6, 7, 5), 
            Array(3, 1, 7, 3, 2), 
            Array(1, 5, 7, 4, 6), 
            Array(8, 1, 9, 2, 6), 
            Array(7, 6, 2, 2, 5)
        );
		obj.sort_major(matrix1);
		//   Case 2
		//   Define matrix of integer elements
		var matrix2: Array[Array[Int]] = Array(
            Array(1, 9, 8, 3, 7), 
            Array(3, -1, 5, 3, 8), 
            Array(1, 3, 5, 6, 11), 
            Array(0, 9, 8, 6, 2), 
            Array(1, 3, 4, 5, 10)
        );
		obj.sort_major(matrix2);
	}
}

Output

  Before Sort Major Diagonal Element
  4  2  6  7  5
  3  1  7  3  2
  1  5  7  4  6
  8  1  9  2  6
  7  6  2  2  5

  After Sort Major Diagonal Element
  1  2  6  7  5
  3  2  7  3  2
  1  5  4  4  6
  8  1  9  5  6
  7  6  2  2  7

  Before Sort Major Diagonal Element
  1  9  8  3  7
  3  -1  5  3  8
  1  3  5  6  11
  0  9  8  6  2
  1  3  4  5  10

  After Sort Major Diagonal Element
  -1  9  8  3  7
  3  1  5  3  8
  1  3  5  6  11
  0  9  8  6  2
  1  3  4  5  10
/* 
  Swift 4 Program
  Sort the major diagonal elements of a matrix
*/
class MyMatrix
{
	//  Display matrix elements
	func show_data(_ matrix: [[Int]], _ size: Int)
	{
		var i: Int = 0;
		while (i < size)
		{
			var j: Int = 0;
			while (j < size)
			{
				print("  ", matrix[i][j], terminator: "");
				j += 1;
			}
			print("\n", terminator: "");
			i += 1;
		}
		print("\n", terminator: "");
	}
	//   Swap diagonal elements of given location
	func swap_node(_ i: Int, _ j: Int, _ matrix: inout[[Int]])
	{
		let temp: Int = matrix[i][i];
		matrix[i][i] = matrix[j][j];
		matrix[j][j] = temp;
	}
	//   Set the minimum value on a given location
	func change_element(_ matrix: inout[[Int]], _ k: Int, _ size: Int)
	{
		var min: Int = k;
		var i: Int = k;
		while (i < size)
		{
			if (matrix[min][min] > matrix[i][i])
			{
				min = i;
			}
			i += 1;
		}
		//   Set the minimum element of [k][k] position
		self.swap_node(k, min, &matrix);
	}
	//   Sort the Major diagonal of a matrix
	func sort_major(_ matrix: inout[[Int]])
	{
		let size: Int = matrix.count;
		//   Not square matrix
		if (matrix[0].count != size || size == 0)
		{
			return;
		}
		//   Display matrix element
		print("  Before Sort Major Diagonal Element");
		self.show_data(matrix, size);
		var k: Int = 0;
		while (k < size)
		{
			self.change_element(&matrix, k, size);
			k += 1;
		}
		//   Display matrix element
		print("  After Sort Major Diagonal Element");
		self.show_data(matrix, size);
	}
}
func main()
{
	let obj: MyMatrix = MyMatrix();
	//   Case 1
	//   Define matrix of integer elements
	var matrix1: [[Int]] = 
    [
		[4, 2, 6, 7, 5] , 
        [3, 1, 7, 3, 2] , 
        [1, 5, 7, 4, 6] , 
        [8, 1, 9, 2, 6] , 
        [7, 6, 2, 2, 5]
	];
	obj.sort_major(&matrix1);
	//   Case 2
	//   Define matrix of integer elements
	var matrix2: [[Int]] = 
    [
		[1, 9, 8, 3, 7] , 
        [3, -1, 5, 3, 8] , 
        [1, 3, 5, 6, 11] , 
        [0, 9, 8, 6, 2] , 
        [1, 3, 4, 5, 10]
	];
	obj.sort_major(&matrix2);
}
main();

Output

  Before Sort Major Diagonal Element
   4   2   6   7   5
   3   1   7   3   2
   1   5   7   4   6
   8   1   9   2   6
   7   6   2   2   5

  After Sort Major Diagonal Element
   1   2   6   7   5
   3   2   7   3   2
   1   5   4   4   6
   8   1   9   5   6
   7   6   2   2   7

  Before Sort Major Diagonal Element
   1   9   8   3   7
   3   -1   5   3   8
   1   3   5   6   11
   0   9   8   6   2
   1   3   4   5   10

  After Sort Major Diagonal Element
   -1   9   8   3   7
   3   1   5   3   8
   1   3   5   6   11
   0   9   8   6   2
   1   3   4   5   10
/* 
  Kotlin Program
  Sort the major diagonal elements of a matrix
*/
class MyMatrix
{
	//  Display matrix elements
	fun show_data(matrix: Array<Array<Int >> , size: Int): Unit
	{
		var i: Int = 0;
		while (i < size)
		{
			var j: Int = 0;
			while (j < size)
			{
				print("  " + matrix[i][j]);
				j += 1;
			}
			print("\n");
			i += 1;
		}
		print("\n");
	}
	//   Swap diagonal elements of given location
	fun swap_node(i: Int, j: Int, matrix: Array<Array<Int>> ): Unit
	{
		var temp: Int = matrix[i][i];
		matrix[i][i] = matrix[j][j];
		matrix[j][j] = temp;
	}
	//   Set the minimum value on a given location
	fun change_element(matrix: Array <Array<Int>> , k: Int, size: Int): Unit
	{
		var min: Int = k;
		var i: Int = k;
		while (i < size)
		{
			if (matrix[min][min] > matrix[i][i])
			{
				min = i;
			}
			i += 1;
		}
		//   Set the minimum element of [k][k] position
		this.swap_node(k, min, matrix);
	}
	//   Sort the Major diagonal of a matrix
	fun sort_major(matrix: Array<Array<Int>> ): Unit
	{
		var size: Int = matrix.count();
		//   Not square matrix
		if (matrix[0].count() != size || size == 0)
		{
			return;
		}
		//   Display matrix element
		print("  Before Sort Major Diagonal Element\n");
		this.show_data(matrix, size);
		var k: Int = 0;
		while (k < size)
		{
			this.change_element(matrix, k, size);
			k += 1;
		}
		//   Display matrix element
		print("  After Sort Major Diagonal Element\n");
		this.show_data(matrix, size);
	}
}
fun main(args: Array < String > ): Unit
{
	var obj: MyMatrix = MyMatrix();
	//   Case 1
	//   Define matrix of integer elements
	var matrix1: Array<Array<Int>> = arrayOf(
        arrayOf(4, 2, 6, 7, 5), 
        arrayOf(3, 1, 7, 3, 2), 
        arrayOf(1, 5, 7, 4, 6), 
        arrayOf(8, 1, 9, 2, 6), 
        arrayOf(7, 6, 2, 2, 5)
    );
	obj.sort_major(matrix1);
	//   Case 2
	//   Define matrix of integer elements
	var matrix2: Array<Array<Int>> = arrayOf(
        arrayOf(1, 9, 8, 3, 7), 
        arrayOf(3, -1, 5, 3, 8), 
        arrayOf(1, 3, 5, 6, 11), 
        arrayOf(0, 9, 8, 6, 2), 
        arrayOf(1, 3, 4, 5, 10)
    );
	obj.sort_major(matrix2);
}

Output

  Before Sort Major Diagonal Element
  4  2  6  7  5
  3  1  7  3  2
  1  5  7  4  6
  8  1  9  2  6
  7  6  2  2  5

  After Sort Major Diagonal Element
  1  2  6  7  5
  3  2  7  3  2
  1  5  4  4  6
  8  1  9  5  6
  7  6  2  2  7

  Before Sort Major Diagonal Element
  1  9  8  3  7
  3  -1  5  3  8
  1  3  5  6  11
  0  9  8  6  2
  1  3  4  5  10

  After Sort Major Diagonal Element
  -1  9  8  3  7
  3  1  5  3  8
  1  3  5  6  11
  0  9  8  6  2
  1  3  4  5  10

Output Explanation

The mentioned C code implements the above algorithm to sort the major diagonal elements of the matrix. It traverses the major diagonal and swaps elements to sort them. The output displays the original matrix and the matrix after sorting the major diagonal.

Time Complexity

The time complexity of the sorting process is O(N^2), where N is the number of rows (or columns) in the matrix. This is because for each element on the major diagonal, we find the minimum element among the remaining diagonal elements, which requires traversing a portion of the matrix. Overall, the algorithm has a quadratic time complexity.

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